My interests lie in probability, conformal invariance and statistical physics.
I have been working on aspects of the Schramm–Loewner evolution (SLE).
Important tools are Brownian motion and related measures on planar curves.

WalkBoundary is
a program to simulate large random walk loops and their boundaries.
This is the same program as you see embedded above,
but the downloadable version is capable of generating much larger loops.
WalkBoundary is available for Mac
or Windows,
or as source code.

All three are interactive animated simulations that you can control using the keyboard and mouse.
(The colours have no meaning beyond tracking the time parametrization in the simulation.)
There is an online version of each simulation (linked above), but the downloadable versions all run much faster, with a larger window on a longer path.
— Mac versions:
Reverse Flow,
Flow Line,
Percolation.
(For controls see “About box”.)
— Windows versions of all three simulations. (For controls see included text files.)
— Source code.

Important note on the Mac versions:
All the Mac programs available here are unsigned.
If the program refuses to run when you double-click it, then you need to right-click on the program's icon and select “Open”.